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Q98 - Modeling Stable Population Size in Gall Aphids

Theoretical B Real exam question - full text reproduced under IBO's CC BY-NC-SA 4.0 license
Ecology

Gall aphids (Pemphigus betae) live in poplar plants. Adult females produce galls on poplar leaves. Some fraction of these galls will emerge and survive to adulthood. Female aphids complete their life cycle after laying eggs in the leaves. All the progeny of a single female aphid are contained in one gall. A student recorded observation on several aphid populations, shown in the table below. All environmental parameters are assumed constant.

Population Number of aborted galls Number of successful galls Female/Male ratio in adult stage
1 35 70 1/1
2 25 75 1/2
3 21 63 Not given
4 16 32 1/1

An equation representing the number of female aphids in the t-th generation is established as below:

Nt = [f × r × (1-m)]^t × N0

Where: Nt = number of adult female aphids in the t-th generation N0 = number of adult female aphids in the initial generation m = fraction mortality of the young aphids f = number of progeny per female aphid r = ratio of female aphids to total adult aphids

Theoretically f, m and r are constant.

Using the information and data, determine which of the statements are true or which are false.

A. Population 1 has a constant number of adult females across generations when each female produces 4 progeny.
B. When every female in population 2 produces 3 progeny, this population will have a constant number of adult females across generations.
C. When population 3 has a constant number of adult females across generations and each female aphid produces 4 progeny, the female/male ratio of the population in adult stage is 1/2.
D. Given that each female in population 4 produces 6 aphids and taking the offspring of population 4 to be in the first generation, the number of adult females in the third generation will be 384.
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Question reproduced from IBO 2016, Theoretical Paper B, licensed under CC BY-NC-SA 4.0 - attributed to the International Biology Olympiad. Open the full exam PDF · Community solutions (unofficial)